[EM] Re: IRV letter

[Bart Ingles]

Chris Benham wrote:
> 
> Bart Ingles wrote:
> >
> >1. Voters submit ranked ballots.
> >2. While no surviving candidate has a top-choice majority:
> >      Eliminate the candidate with the greatest plurality of
> >first-choice votes.
> >(End definition)
> >
> >Example:
> >3  A > B > C
> >49 B > C > A
> >48 C > B > A
> >
> >Round 1: No candidate has 50% + 1, so B is eliminated.
> >Round 2: C wins with a 97% 'majority'.
> >
> >The method does appear to meet Majority Favorite and Condorcet Loser.
> >
> CB: Yes it does. But it fails two other Woodall criteria that are met by
> IRV,  "Plurality" and  Mono-add-top.
> His Plurality criterion says that if  candidate A has more first-place
> votes than candidate B has non-last-place votes, then
> B cannot be elected. In your example, B has more first preferences than
> C has non-last preferences, so  the Plurality Criterion
> says  "not C".

BI:
I don't mean to nitpick, but B has only 49 first preferences, while C
has 97 non-last preferences.  While the hypothetical method may not
guarantee Plurality compliance, the above doesn't appear to be an
example of failure.

If Woodall's Plurality doesn't guard against the outcome above, it
should be possible to modify the method so it passes Plurality along
with the majoritarian criteria by changing step 2 to read:

"2. While no surviving candidate has a top-choice majority, eliminate
the candidate with the greatest plurality of first-choice votes in which
said plurality does not exceed the number of non-last-choice votes of
any other candidate."

Bart